We start by exploring how players fare in one of the most basic and well-studied social dilemmas, the donation game [1]}. Here, cooperation means paying a cost \(c\!>\!0\)  to deliver a benefit of \(b\!>\!c\)  to the co-player. The resulting payoffs yield a prisoner's dilemma. Players individually prefer to defect, yet mutual cooperation yields a better payoff than mutual defection. Players start out with random memory-one strategies (Fig. REF a) and the game is repeated for many rounds (see Methods). Previous work shows that this game allows for four types of symmetric equilibria among memory-one players [2]}: players may either both cooperate, both defect, alternate, or apply so-called equalizers [3]}, [4]}.
<FIGURE>